Using graph convolutional networks to approximate cardinality constraints in portfolio optimization

Abstract

Cardinality constraint has been widely adopted for portfolio optimization to reduce the transaction cost and monitoring cost. In such problem, several methods were developed to avoid the occurring NP-hardness of the problem. However, most of them were unable to reach to solve the cardinality-constrained portfolio optimization in very short time. In this paper, we introduced Graph Convolutional Network to learn the asset selection of the problem to approximate the optimal solution of the cardinality-constrained portfolio optimization. Furthermore, a method to understand a correlation matrix as a weighted adjacency matrix has been developed in this paper. Lastly, we compared the optimality and time consumption of our method to the ones from common practice.